Question: Which of the following numbers is a multiple of 11? ${89,96,99,103,113}$
Solution: The multiples of $11$ are $11$ $22$ $33$ $44$ ..... In general, any number that leaves no remainder when divided by $11$ is considered a multiple of $11$ We can start by dividing each of our answer choices by $11$ $89 \div 11 = 8\text{ R }1$ $96 \div 11 = 8\text{ R }8$ $99 \div 11 = 9$ $103 \div 11 = 9\text{ R }4$ $113 \div 11 = 10\text{ R }3$ The only answer choice that leaves no remainder after the division is $99$ $ 9$ $11$ $99$ We can check our answer by looking at the prime factorization of both numbers. Notice that the prime factors of $11$ are contained within the prime factors of $99$ $99 = 3\times3\times11 11 = 11$ Therefore the only multiple of $11$ out of our choices is $99$. We can say that $99$ is divisible by $11$.